I am going to Stockholm for 10 days. I do not drive, so I would like to know what is the most cost-effective way to use public transportation? Is there e.g. a weekly/monthly pass that I can buy once and use anywhere? (I tried to look at websites but everything I found was in Swedish...)
Stockholm has an excellent web site in English that explains all the details and even has a well made and reasonably funny video to explain it. See https://sl.se/en/getting-around/ https://www.youtube.com/watch?v=HbKTjOjcWos
Tickets and fares are explained here https://sl.se/en/fares--tickets/
Which one is the most efficient for you depends on how often and how far you want to travel. We can't know this, so you need to assess this yourself.
You can find an SL center at the T-Centralen of Stockholm, where you can buy tickets (cards with chip) and also discuss what options there are. Tickets are also sold at certain convenience stores, (Pressbyran). The public transportation is good, but sometimes there might be issues (yesterday, two major stations closed down due to rust in the new escalators - yes, really!).